Let (5 + 3√2 ) be a rational number
5 + 3√2 = P / q
(Where q ≠ 0 and p and q are co- prime number)
3√2 = P / q - 5
√2 = (p -5q )/ 3q
p and q are integers and g ≠ 0
(p -5q) / 3q is rational number
√2 is a rational number but √2 is irrational number.
This contradiction has arisen because our assumption is wrong. So we conclude that (5+3√2) is an irrational number.
